Hypersurfaces with constant mean curvature and prescribed area |
| |
Authors: | Frank Duzaar |
| |
Affiliation: | 1. Institut für Reine Mathematik, Humboldt-Universit?t zu Berlin, Sitz: Ziegelstr. 13A, 10099, Berlin
|
| |
Abstract: | Summary We consider—in the setting of geometric measure theory—hypersurfacesT (of codimension one) with prescribed boundaryB in Euclideann+1 space which maximize volume (i.e.T together with a fixed hypersurfaceT 0 encloses oriented volume) subject to a mass constraint. We prove existence and optimal regularity of solutionsT of such variational problems and we show that, on the regular part of its support,T is a classical hypersurface of constant mean curvature. We also prove that the solutionsT become more and more spherical as the valuem of the mass constraint approaches ∞. This work was done at the Centre for Mathematics and its Applications at the Australian National University, Canberra while the author was a visiting member This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag. |
| |
Keywords: | 49F22 53A10 53C42 |
本文献已被 SpringerLink 等数据库收录! |
|